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In this work, I study the non-linear QED effects to the Maxwell equations due to the interaction of the electromagnetic waves with an external magnetic field with arbitrary direction with respect to the direction of propagation of the electromagnetic waves. I show that in the case when the external magnetic field has a longitudinal component with respect to the electromagnetic wave direction of propagation, a longitudinal photon state is generated in a magnetized vacuum. The mixing of transverse and longitudinal photon states causes a decrease in the group velocity with respect to the velocity of electromagnetic waves in a vacuum. In a cosmological context, as far as a cosmic magnetic field is concerned, the decrease of the group velocity of any form of electromagnetic radiation would cause changes in several distance measures in cosmology. The most affected of these distance measures turn out to be the comoving distance and the luminosity distance. The absolute change in distance measures are usually large but the relative changes are very small., Comment: 13 pages

In this work, I study the mixing of photons with pseudoscalar particles and vice-versa in the presence of an external magnetic field and a pseudoscalar field. I solve exactly for the first time in the literature the equations of motion of the electromagnetic field coupled with a pseudoscalar field in the presence of a constant magnetic field with arbitrary direction with respect to the direction of propagation of the fields in vacuum. In addition, I also solve exactly the equations of motion in a magnetized plasma/gas for perpendicular propagation with respect to the external magnetic field. By finding exact solutions to the equations of motion, I find exact expressions for the transition efficiencies of photons into pseudoscalar particles in different situations. The expressions of the transition efficiencies generalize and correct those previously found in the literature by using approximate WKB methods on solving the equations of motion. In the case when the direction of propagation of fields with respect to the external magnetic field is not perpendicular, a longitudinal state of the electromagnetic field is generated even in a magnetized vacuum. The appearance of the longitudinal electric field state could be used for laboratory searches of pseudoscalar particles such as the axion and/or axion-like particles., Comment: Published version to EPJC. Unchanged results

In this work I study the effect of graviton-photon mixing in a constant external magnetic field and find for the first time in the literature exact solution of the equations of motion. In particular, I apply the effect of graviton-photon mixing to the case of interaction of gravitational waves with an external magnetic field and calculate the intensity Stokes parameter of the produced electromagnetic radiation. The obtained results are new and extend previous results obtained by using approximation methods., Comment: 9 pages. A typo present in Eq. (19) which also propagated to Eq. (20) and Eq. (22) has been fixed. This typo was a missing $\omega^2$ in these equations

In this work, we present the first experimental upper limits on the presence of stochastic ultra-high-frequency gravitational waves. We exclude gravitational waves in the frequency bands from $(2.7 - 14)\times10^{14}~$Hz and $(5 - 12)\times10^{18}~$Hz down to a characteristic amplitude of $h_c^{\rm min}\approx6\times 10^{-26}$ and $h_c^{\rm min}\approx 5\times 10^{-28}$ at $95~$% confidence level, respectively. To obtain these results, we used data from existing facilities that have been constructed and operated with the aim of detecting WISPs (Weakly Interacting Slim Particles), pointing out that these facilities are also sensitive to gravitational waves by graviton to photon conversion in the presence of a magnetic field. The principle applies to all experiments of this kind, with prospects of constraining (or detecting), for example, gravitational waves from light primordial black hole evaporation in the early universe.

Generation of cosmic microwave background (CMB) elliptic polarization due to the Cotton-Mouton (CM) effect in a cosmic magnetic field is studied. We concentrate on the generation of CMB circular polarization and on the rotation angle of the CMB polarization plane from the decoupling time until at present. For the first time, a rather detailed analysis of the CM effect for an arbitrary direction of the cosmic magnetic field with respect to photon direction of propagation is done. Considering the CMB linearly polarized at the decoupling time, it is shown that the CM effect is one of the most substantial effects in generating circular polarization especially in the low part of the CMB spectrum. It is shown that in the frequency range $10^8$ Hz $\leq \nu_0\leq 10^9$ Hz, the degree of circular polarization of the CMB at present for perpendicular propagation with respect to the cosmic magnetic field is in the range $ 10^{-13}\lesssim P_C(t_0)\lesssim 7.65\times 10^{-7}$ or Stokes circular polarization parameter $2.7 \times 10^{-13}$ K $\lesssim |V(t_0)|\lesssim 2 \times 10^{-6}$ K for values of the cosmic magnetic field amplitude at present in the range $10^{-9}$ G $\lesssim B\lesssim 8\times 10^{-8}$ G. On the other hand, for not perpendicular propagation with respect to the cosmic magnetic field we find $10^{-15}\lesssim P_C(t_0)\lesssim 6\times 10^{-12}$ or $2.72 \times 10^{-15}$ K $\lesssim |V(t_0)| \lesssim 10^{-11}$ K, for the same values of the cosmic magnetic field amplitude and same frequency range. Estimates on the rotation angle of the CMB polarization plane $\delta\psi_0$ due to the CM effect and constraints on the cosmic magnetic field amplitude from current constraints on $\delta\psi_0$ due to a combination of the CM and Faraday effects are found., Comment: Version published in European Physical Journal C. With respect to version (v1), in this version (v2) several typos have been corrected through the text. Unchanged results

In the era of gravitational wave (GW) detection from astrophysical sources by LIGO/VIRGO, it is of great importance to take the quantum gravity effect of graviton-photon (GRAPH) mixing in the cosmic magnetic field to the next level. In this work, we study such an effect and derive for the first time perturbative solutions of the linearized equations of motions of the GRAPH mixing in an expanding universe. In our formalism we take into account all known standard dispersive and coherence breaking effects of photons such as the Faraday effect, the Cotton-Mouton (CM) effect, and the plasma effects in the cosmic magnetic field. Our formalism, applies to a cosmic magnetic field either a uniform or a slowly varying non-homogeneous field of spacetime coordinates with an arbitrary field direction. For binary systems of astrophysical sources of GWs at extragalactic distances with chirp masses $M_\text{CH}$ of a few solar masses, GW present-day frequencies $\nu_0\simeq 50-700$ Hz, and present-day cosmic magnetic field amplitudes $\bar B_0\simeq 10^{-10}-10^{-6}$ G, the power of electromagnetic radiation generated in the GRAPH mixing at present is substantial and in the range $P_\gamma\simeq 10^6-10^{15}$ (erg/s). On the other hand, the associated power flux $F_\gamma$ is quite faint depending on the source distance with respect to the Earth. Since in the GRAPH mixing the velocities of photons and gravitons are preserved and are equal, this effect is the only one known to us, whose certainty of the contemporary arrival of GWs and electromagnetic radiation at the detector is guaranteed., Comment: Published version in Physical Review D. In the published version the title has been changed by the editors to 'Graviton-Photon mixing' instead of 'GRAPH mixing'. With respect to (v1), in this version (v2), typos have been corrected, new references have been added and an additional section (sec.8) has been added. Typos in Eqs. (40) and (41) have been fixed

The vacuum polarization in an external gravitational field due to one loop electron-positron pair and one loop millicharged fermion-antifermion pair is studied. Considering the propagation of electromagnetic (EM) radiation and gravitational waves (GWs) in an expanding universe, it is shown that by taking into account QED effects in curved spacetime, the propagation velocity of photons is superluminal and can exceed that of gravitons. We apply these results to the case of the GW170817 event detected by LIGO. If the EM radiation and GWs are emitted either simultaneously or with a time difference from the same source, it is shown that the EM radiation while propagating with superluminal velocity, would be detected either in advance or in delay with respect to GW depending on the ratio of millicharged fermion relative charge to mass $\epsilon/m_\epsilon$., Comment: Version to be published in JCAP. With respect to the previous version (v2), in this version (v3) the text has been sectioned and typos have been corrected. As required by the referee, a comparison of our results with the current limits on the millicharged fermions has been done

Generation of magneto-optic effects by the interaction of the CMB with cosmic magnetic fields is studied. Effects which generate polarization such as the Cotton-Mouton effect, vacuum polarization and photon-pseudoscalar mixing in external magnetic field are studied. Considering the CMB linearly polarized at decoupling time, it is shown that photon-pseudoscalar mixing in external magnetic field, the Cotton-Mouton effect in plasma and the vacuum polarization in cosmic magnetic field, would generate elliptic polarization of the CMB depending on the photon frequency and magnetic field strength. Among standard magneto-optic effects, the Cotton-Mouton effect in plasma turns out to be the dominant effect in the generation of CMB elliptic polarization in the low frequency part $\nu_0 \sim 10^8-10^9$ Hz with degree of circular polarization $P_C(T_0)\simeq 10^{-10}-10^{-6}$ for magnetic field amplitude $B_{e0}\sim 100\, \text{nG}-1$ nG. The vacuum polarization in magnetic field is the dominant process in the high frequency part $\nu_0\geq 10^{10}$ Hz where the degree of circular polarization at present is $P_C(T_0)\lesssim 10^{-11}$ in the best scenario. It is shown that photon-pseudoscalar particle mixing in cosmic magnetic field generates elliptic polarization of the CMB as well and even in the case of initially unpolarized CMB. New limits/constraints on the pseudoscalar parameter space are found. By using current limit on the degree of circular polarization of the CMB, the upper limit of $|g_{\phi\gamma}|<4.29\times 10^{-19}(\text{G}/B_{e0})$ GeV$^{-1}$ for $m_\phi<1.6\times 10^{-14}$ eV in the weak mixing case is found. If $|g_{\phi\gamma}| < 1.17\times 10^{-24}(\text{G}/B_{e0})$ GeV$^{-1}$, a value of the order $|g_{\phi\gamma}|\simeq 10^{-26}(\text{G}/B_{e0})$ GeV$^{-1}$ for $m_\phi\simeq 1.6\times 10^{-14}$ eV in the resonant case, from large scale temperature anisotropy is obtained., Comment: Matches the published version in Nuclear Physics B

Axion production due to photon-axion mixing in tangled magnetic field(s) prior to recombination epoch and magnetic field damping can generate cosmic microwave background (CMB) spectral distortions. In particular, contribution of both processes to CMB $\mu$ distortion in the case of resonant photon-axion mixing is studied. Assuming that magnetic field power spectrum is approximated by a power law $P_B(k)\propto k^n$ with spectral index $n$, it is shown that for magnetic field cut-off scales $172.5$ pc $\leq \lambda_B\leq 4\times 10^3$ pc, axion contribution to CMB $\mu$ distortion is subdominant in comparison with magnetic field damping in the cosmological plasma. Using COBE upper limit on $\mu$ and for magnetic field scale $\lambda_B\simeq 415$ pc, weaker limit in comparison with other studies on the magnetic field strength ($B_0\leq 8.5\times 10^{-8}$ G) up to a factor 10 for the DFSZ axion model and axion mass $m_a\geq 2.6\times 10^{-6}$ eV is found. A forecast for the expected sensitivity of PIXIE/PRISM on $\mu$ is also presented., Comment: Typos corrected. Requested by the referee some additional text has been added. Minor changes. Version to be published at EPJ C

The oscillation of the CMB photons into axions can cause CMB spectral distortion in the presence of large scale magnetic field. With the COBE limit on the $\mu$ parameter and a homogeneous magnetic field with strength $B\lesssim 3.2$ nG at the horizon scale, an upper limit on the axion mass is found to be, $m_a\lesssim 4.8\times 10^{-5}$ eV for the KSVZ axion model. On the other hand, using the value of excluded axion mass $m_a\simeq 3.5\times 10^{-6}$ eV from the ADMX experiment together with the COBE bound on $\mu$, is found $B\simeq 46$ nG for the KSVZ axion model and $B\simeq 130$ nG for DFSZ axion model, for a homogeneous magnetic field with coherence length at the present epoch $\lambda_B\simeq 1.3$ Mpc. Forecast on $B$ and $m_a$ for PIXIE/PRISM expected sensitivity on $\mu$ are derived. If CMB $\mu$ distortion would be detected by the future space missions PIXIE/PRISM and assuming that the strength of the large scale magnetic field is close to its canonical value, $B\simeq 1-3$ nG, axions in the mass range $2\, \mu$eV - $3\, \mu$eV would be potential candidates of CMB $\mu$-distortion., Comment: Corrected inequality typos in the abstract. Minor changes

Transformation of CMB photons into light pseudoscalar particles at post big bang nucleosynthesis epoch is considered. Using the present day value of a large scale magnetic field to estimate it at earlier cosmological epochs, the oscillation probability of photons into light pseudoscalar particles with an account of coherence breaking in cosmological plasma is calculated. Demanding that the photon transformation does not lead to an exceedingly large CMB spectral distortion and temperature anisotropy, the constraints on the coupling constant of axion like particles to photons, $ g_{\phi\gamma} B \lesssim (10^{-15} - 10^{-12}) \textrm{nG}\times \textrm{GeV}^{-1}$, are found for the axion like particle mass in the interval $10^{-25}$ eV $\lesssim m_{\phi}\lesssim 10^{-5}$ eV, where $B$ is the strength of the large scale magnetic field at the present time. Our results update the previously obtained ones since we use the density matrix formalism which is more accurate than the wave function approximation for the description of oscillations with an essential coherence breaking. In the axion like particle mass range $10^{-25}$ eV $\lesssim m_{\phi}\lesssim 10^{-14}$ eV, weaker limits, by at least 2 orders of magnitude $g_{\phi\gamma} B \lesssim 10^{-11}\textrm{nG}\times \textrm{GeV}^{-1}$, are obtained in comparison with the wave function approximation. In the mass range $10^{-14}$ eV $\lesssim m_{\phi}\lesssim 10^{-5}$ eV, on the other hand, limits that are stronger, by more than an order of magnitude are obtained. Our results are derived by using upper limits on spectral distortion parameter $\mu$ and temperature anisotropy $\Delta T/T$ found by COBE and expected sensitivities by PIXIE/PRISM., Comment: Published version

Here I discuss the conversion of relic gravitons into photons in large scale cosmological magnetic fields. It is shown that the conversion probability is quite large at the post recombination epoch with a rather large density of formed photons. The produced electromagnetic radiation could make a substantial contribution to the cosmic extragalactic background light and even explain the cosmic x ray background excess., Comment: 4 pages, 3 figures. Talk presented at the "25th Rencontres de Blois, Particle Physics and Cosmology" 26-31 May 2013. To be published at the conference preceedings

Conversion of the CMB photons into gravitational waves at the post recombination epoch is considered. We calculate the probability of transformation of the CMB photons into gravitons in the presence of a large scale magnetic field. Based on the present day limits on the strength of the large scale magnetic field we show that the probability of the produced gravitons as a result of photon to graviton conversion is reasonable and such mechanism would produce an isotropic background of gravitational waves in the same frequency range of the CMB photons. The mechanism proposed would be a rather good opportunity to study the high frequency part of the spectrum of gravitational waves., Comment: 7 pages, 6 figures, minor changes and new references have been added; published version

Resonant conversion of high energy gravitons into photons in large scale cosmological magnetic fields at the post recombination epoch is considered. It is shown that the probability of the resonance photon production is much higher than the non-resonant one. As a result an observable isotropic background of cosmic gamma rays might be created. As shown in our previous paper, an early population of primordial black holes (PBHs) prior to big bang nucleosynthesis (BBN) could be an efficient source of high frequency gravitational waves. For the primordial black hole mass about $10^8$ g the produced photons would be the dominant component of the soft to hard Cosmic X-ray Background (CXB) and for lower masses the spectrum is shifted down to the ultraviolet and optic., Comment: 16 pages, 11 figures, more references has been added. Published version

Conversion of gravitational waves into electromagnetic radiation is discussed. The probability of transformations of gravitons into photons in presence of cosmological background magnetic field is calculated at the recombination epoch and during subsequent cosmological stages. The produced electromagnetic radiation is concentrated in the X-ray part of the spectrum. It is shown that if the early Universe was dominated by primordial black holes (PBHs) prior to Big Bang Nucleosynthesis (BBN), the relic gravitons emitted by PBHs would transform to an almost isotropic background of electromagnetic radiation due to conversion of gravitons into photons in cosmological magnetic fields. Such extragalactic radiation could be noticeable or even dominant component of Cosmic X-ray Background., Comment: 24 pages, 8 figures and 1 table; minor changes and more references have been added

The energy density of relic gravitational waves (GWs) emitted by primordial black holes (PBHs) is calculated. We estimate the intensity of GWs produced at quantum and classical scattering of PBHs, the classical graviton emission from the PBH binaries in the early Universe, and the graviton emission due to PBH evaporation. If nonrelativistic PBHs dominated the cosmological energy density prior to their evaporation, the probability of formation of dense clusters of PBHs and their binaries in such clusters would be significant and the energy density of the generated gravitational waves in the present day universe could exceed that produced by other known mechanisms. The intensity of these gravitational waves would be maximal in the GHz frequency band of the spectrum or higher and makes their observation very difficult by present detectors but also gives a rather good possibility to investigate it by present and future high frequency gravitational waves electromagnetic detectors. However, the low frequency part of the spectrum in the range $f\sim 0.1-10$ Hz may be detectable by the planned space interferometers DECIGO/BBO. For sufficiently long duration of the PBH matter dominated stage the cosmological energy fraction of GWs from inflation would be noticeably diluted., Comment: 32 pages, 4 figures; according to the referee comments some inaccurate statements are corrected and high frequency detectors of gravitational waves are briefly discussed